An Approximate Solution for a Class of Ill-Posed Nonhomogeneous Cauchy Problems

In this paper, we consider a nonhomogeneous differential operator equation of first order u ′ t + A u t = f t . The coefficient operator A is linear unbounded and self-adjoint in a Hilbert space. We assume that the operator does not have a fixed sign. We associate to this equation the initial or final conditions u 0 = Φ or u T = Φ . We note that the Cauchy problem is severely ill-posed in the sense that the solution if it exists does not depend continuously on the given data. Using a quasi-boundary value method, we obtain an approximate nonlocal problem depending on a small parameter. We show that regularized problem is well-posed and has a strongly solution. Finally, some convergence results are provided.

Identifying the competencies of China’s paediatric residents: a modified Delphi method study

PurposeStandardised Training of Paediatric Resident (STPR) plays an essential role in training qualified paediatricians. Until now, China had no paediatric resident competency index system to effectively guide and evaluate the competence of paediatric residents. This study aimed to establish a competency index system for paediatric residents in China to provide a reference for improving the training system and quality of STPR.Study design and settingThis study conducted two rounds of Delphi expert consultation survey among paediatric medical experts (n=16), followed by screening, revising and supplementing indicators using the boundary value method. Next, the analytic hierarchy process was used to determine the weight of indicators and finally establish a competency index system for paediatric residents.ResultsThe results of the statistical analysis revealed a positive coefficient of 100% for both rounds of expert consultation. The expert authority coefficient values were 0.82 and 0.83, and the expert coordination coefficient test was p<0.01. After referring to experts’ opinions, a competency index system for paediatric residents with 5 primary indicators, 14 secondary indicators and 73 tertiary indicators was finally formed and the weight of each indicator was calculated. The five primary indicators were professional quality (0.3187), knowledge and skills (0.2734), communication and cooperation (0.1986), lifelong learning (0.1302), and teaching ability (0.0791).ConclusionsIn this study, a competency index system for paediatric residents was constructed following the characteristics and quality requirements for paediatric residents in China and is expected to significantly improve the overall level of paediatricians’ medical service quality and supply.

Problems of developing the model for forming parent machine-building enterprise order portfolio under cooperation conditions

The article deals with the feature’s projects portfolio formation of head enterprise that produces high-tech products. Methods the projects portfolio formation are considered: mathematical, simulation and economic-statistical. The factors that influence the choice of the model are illustrated.It is proposed to carry out research on the basis of creation complexes ofinterrelated, multi-level models and optimization-simulation approach. Themeans of implementing this approach are human-machine iterative,interactive procedures. To find the optimal solution by the decision maker,procedures should be based on the identification of the main goals andpreferences used in the creation of an optimal of the project portfolio, thestudy of a set of acceptable parameters and actions. The head enterprise is considered as a complex system described by severalmodels, to which the control scheme with direct and feedback is applicable,where: functional breakdown of the process of forming the projects portfolio into separate blocks justifies the use of multi-level modeling of a complex production system; in long-term planning and forecasting, it is necessary to solve both the direct problem of system consequences for a given “input”, and the inverse problem of planning, which has a significant spread of output parameters. In order to optimize the method, it is proposed to create iteration- optimization analytical models using the two-point boundary value method, including planning from the achieved and planning from the final result. Indicated the advantages of using a specialized mathematical apparatus inthe formation of the projects portfolio.